Polynomial Regression

It is not necessary for us to always use only the features that we have. If needed, we can sometimes create new features using the existing ones that might be more suitable for the given problem.

For example, if we have length and width, we can use them to form a new feature named area and perform linear regression using this new feature.

Polynomial Regression is very similar to multivariate linear regression. Each $x_i$ could be a degree of a given feature.

For example,

$h_\theta(x) = \theta_0 + \theta_1x_1 + \theta_2x_2 + \theta_3x_3$

where $x_1 = size, \, x_2=(size)^2, \, x_3=(size)^3$

However, while using Polynomial Regression, it is very important to scale the features for gradient descent to work properly.

We can decide to use Polynomial Regression in any manner, i.e. we can even write our hypothesis as:

$h_\theta(x) = \theta_0 + \theta_1(size) + \theta_2(size)^{1/2} + \theta_3(size)^{1/3}$

Later, we discuss how certain algorithms help us in choosing what features to use and how to use them efficiently.